It is known that the half life of p53 is short and so does that play a role in the amount of energy the cell would need to expend to degrade all the p53? By that does the fact that the half life of p53 is so short does that just allow for the cell to not have to expend very much energy to degrade the p53 so in a way the cell doesn't "mind" having to degrade the p53 since it wouldn't take a lot of effort?
This answer is not reserved for the example you cite but for all proteins/RNAs which have high turnover. So your question generalizes to
What is the advantage of having high turnover? or in other words, What is the advantage of regulation via degradation?
- Fast responsiveness. If your protein/RNA has a low turnover then it would take a lot of time for it to clear up from the cytoplasm even after the activating signal is gone. Enhancing the degradation will make the response fast. Cell cycle proteins such as p53 have to clear up as soon as the cell progresses to the next phase.
- In certain cases an additional degradation control makes the regulation more efficient. If the "regulated" gene happens to be in turn an activator of many downstream genes, then efficient control actually helps in saving the cellular resources. I can't cite any literature for it but I have observed this in one of my unpublished research work using mathematical models.